What is the main conflict in Poirot Investigates by Agatha Christie?

Captain Hastings, Poirot's friend, notices a woman on the street when looking through the window of Poirot's room. Poirot identifies her to be Miss Mary Marvell, a famous American film star. He suspects she is on the way to see him. Soon his predictions are confirmed, and the door bell rings. Mary Marvell brings threatening letters she received in relation to the diamond in her possession called the "Western Star."